On one extremal problem for positive series

  • O. I. Stepanets
  • A. L. Shydlich

Abstract

The approximation properties of the spaces $S^p_{\varphi}$ introduced by Stepanets’ were studied in a series of works of Stepanets’ and his disciples. In these works, problems related to the determination of exact values of $n$-term approximations of $q$-ellipsoids in these spaces were reduced to some extremal problems for series with terms that are products of elements of two nonnegative sequences one of which is fixed and the other varies on a certain set. Since solutions of these extremal problems may be of independent interest, in the present work we develop a new method for finding these solutions that enables one to obtain the required result in a substantially shorter and more transparent way.
Published
25.12.2005
How to Cite
StepanetsO. I., and ShydlichA. L. “On One Extremal Problem for Positive Series”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, no. 12, Dec. 2005, pp. 1677–1683, https://umj.imath.kiev.ua/index.php/umj/article/view/3718.
Section
Research articles